A gain-field encoding of limb position and velocity in the internal model of arm dynamics.

Hwang EJ, Donchin O, Smith MA, Shadmehr R - PLoS Biol. (2003)

Bottom Line:
The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

ABSTRACTAdaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.

pbio.0000025-g004: Gain-Field Representation Reproduces Previously Reported Patterns of Spatial Generalization(A) Figure 4A from Shadmehr and Moussavi (2000). The right workspace is separated from the left workspace by 80 cm. Each histogram bar is average maximum PE of 64 movements. Smaller errors of trained group than those of control group at right workspace indicate the transfer of learning from left to right workspace.(B) Simulation results in the same format as (A); correlation coefficient to subject data is 0.89.(C) A spring-like force field, F→ = K·x→ (K = [0 −55;55 0] N/m), was used for simulation.(D) Hand path trajectories in field trials from the first set in the spring-like force field. Each set consists of 192 center-out movements. Targets are given at eight positions on 10 cm circumference in pseudorandom order.(E) Hand path trajectories in field trials from the fifth set of training.(F) Hand path trajectories of catch trials from the fifth set.

Mentions:
In the Shadmehr and Moussavi experiment (2000), subjects trained in a clockwise viscous curl-field (F = B·ẋ, B = [0 − 13;13 0] N m/s) in the “left workspace” (shoulder in a flexed posture) and were then tested in the same field with the hand in a workspace 80 cm to the right (shoulder in an extended posture). The idea was to see whether there is any generalization of learning from the left workspace to the right workspace. Since the viscous curl-field perturbed the subject's hand in the perpendicular direction of hand velocity, as a movement error, they measured the maximum perpendicular displacement from the straight line connecting start and target position. For a direct comparison, we used the same measure, maximum PE, shown in Figure 4. During the left workspace training, the movement errors decreased (Figure 4A). After the training on the left workspace, Shadmehr and Moussavi (2000) tested these subjects in the right workspace. Their errors on the right are significantly smaller than the errors of control subjects, who did not train on the left, indicating a transfer of adaptation from the left workspace to right (Figure 4A). When confronted with the same protocol, the bases that had fit out data in Figure 3 produced a pattern of generalization across large distances that was quite similar to that of the subjects' generalization (Figure 4B; correlation coefficient = 0.89).

pbio.0000025-g004: Gain-Field Representation Reproduces Previously Reported Patterns of Spatial Generalization(A) Figure 4A from Shadmehr and Moussavi (2000). The right workspace is separated from the left workspace by 80 cm. Each histogram bar is average maximum PE of 64 movements. Smaller errors of trained group than those of control group at right workspace indicate the transfer of learning from left to right workspace.(B) Simulation results in the same format as (A); correlation coefficient to subject data is 0.89.(C) A spring-like force field, F→ = K·x→ (K = [0 −55;55 0] N/m), was used for simulation.(D) Hand path trajectories in field trials from the first set in the spring-like force field. Each set consists of 192 center-out movements. Targets are given at eight positions on 10 cm circumference in pseudorandom order.(E) Hand path trajectories in field trials from the fifth set of training.(F) Hand path trajectories of catch trials from the fifth set.

Mentions:
In the Shadmehr and Moussavi experiment (2000), subjects trained in a clockwise viscous curl-field (F = B·ẋ, B = [0 − 13;13 0] N m/s) in the “left workspace” (shoulder in a flexed posture) and were then tested in the same field with the hand in a workspace 80 cm to the right (shoulder in an extended posture). The idea was to see whether there is any generalization of learning from the left workspace to the right workspace. Since the viscous curl-field perturbed the subject's hand in the perpendicular direction of hand velocity, as a movement error, they measured the maximum perpendicular displacement from the straight line connecting start and target position. For a direct comparison, we used the same measure, maximum PE, shown in Figure 4. During the left workspace training, the movement errors decreased (Figure 4A). After the training on the left workspace, Shadmehr and Moussavi (2000) tested these subjects in the right workspace. Their errors on the right are significantly smaller than the errors of control subjects, who did not train on the left, indicating a transfer of adaptation from the left workspace to right (Figure 4A). When confronted with the same protocol, the bases that had fit out data in Figure 3 produced a pattern of generalization across large distances that was quite similar to that of the subjects' generalization (Figure 4B; correlation coefficient = 0.89).

Bottom Line:
The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace.Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones.We confirmed these predictions experimentally.

ABSTRACTAdaptability of reaching movements depends on a computation in the brain that transforms sensory cues, such as those that indicate the position and velocity of the arm, into motor commands. Theoretical consideration shows that the encoding properties of neural elements implementing this transformation dictate how errors should generalize from one limb position and velocity to another. To estimate how sensory cues are encoded by these neural elements, we designed experiments that quantified spatial generalization in environments where forces depended on both position and velocity of the limb. The patterns of error generalization suggest that the neural elements that compute the transformation encode limb position and velocity in intrinsic coordinates via a gain-field; i.e., the elements have directionally dependent tuning that is modulated monotonically with limb position. The gain-field encoding makes the counterintuitive prediction of hypergeneralization: there should be growing extrapolation beyond the trained workspace. Furthermore, nonmonotonic force patterns should be more difficult to learn than monotonic ones. We confirmed these predictions experimentally.